You say your question is about Rumbles but, IME, the writing you refer to has been applied to most
all Fender products at one time or another. And, it may
seem true in certain circumstances. F'rinstance, the Fender guitar amps got a reputation early on for being "as piercing as ice-picks" due to their lack of distortion thru most of their volume range. That was especially true when using Fender's likewise piercing single-coil pickup guitars! Hence the need to really crank Fender guitar amps to get the oft-desired warm, or even hairy, distorted guitar tone. Nothing special? Hmmph! It was a significantly cleaner flavor than most expected, and it took some getting used to.
Some believe this contributed to the use of early Fender Bassman amps with guitar to get a richer guitar tone from the more bassy circuit and/or bassy speakers. Meanwhile, others were promoting their more distorted (cheaper to produce?) amps and pickups as having that "more flavorful" tone. Lemons to lemonade, eh?
Then, Fender Stratocasters had been pidgeonholed into that clean, reverby surf sound when "that left-handed British black guy" invaded America with a Strat and a few FX pedals. Suddenly, that clean Fender sound was in demand, since it could be dirtied up to taste and still cleaned up nicely!
Though, admittedly, the CBS-owned Fender company never did any significant bass amp development, while Ampeg and others were very actively pushing the loud & heavy rock bass scene. Thus Fender bass amps got the reputation for being underpowered with weak speakers, compared to the more powerful bass amps of the '70s and '80s. But most admitted, however, that the Bassman had great tone at low volumes.
Then, in the mid-'90s came
the very first Fender Rumble bass amp from their Custom Shop! Now, this was a serious 300 watt all tube head sitting on a couple of serious 4x12 cabs, some including
subwoofers! I get the feeling it was limited Custom Shop production without the venerable Bassman name in order to test the marketing waters. Well, it must have been deemed a success as the 300 watt Bassman later appeared with real bass tuned drivers! Late to the modern bass party, and hard to shake old perceptions, but a real player nonetheless.
Then(!), the Rumble name returned in the early 2000s, but was relegated to Fender's "value line" of small solid state bass amps, while the Bassman name carried on what the first Rumble started! Again, maybe as a test, Rumbles had something to prove in
this new incarnation (V1) as cheap, beginners, or practice, bass amps. "Hey, how 'bout adding a sound sensitive pulsing red light in the port?", somebody said. Are you kidding me?!? Why not just print the word "toy" on the nameplate!?! But, slowly, over time, the Rumbles gained market share with reliability and versatility of good tone at an affordable price. And this was enough to justify more powerful 150 watt & 350 watt amps and very good speakers in
the second version (V2). Until, finally,
the third version of Rumbles (V3) got the retro Bassman cosmetics and some really serious, 500 watt power and ultra lightweight cabs, that took off like wildfire! The V3 Rumbles are now crowned with the 800 watt, 2 ohm stable, 800 HD and three 3rd generation bass modeling amps, the LT25, Studio 40 & Stage 800.
Nothing special? No nuance or flavor? Well, It's hard to argue with success, but detractors will always try, and you'll never convince some people with words. I, for one, never gave a serious thought to the V1 or V2 Rumbles, and expected my trial of the V3 R500c to fall flat. "
But if you saw my face? Now I'm a believer!"
Sorry for the rant.
ps: I'm considering getting a
cool V1 Rumble 25 with the pulsing red light!
.
.
But, hopefully it will also be part of the joyful reunion in France. 
And it should be a good score of some used Rumbles for some other(s) here in the states. 
